摘要
对有限变形下线弹性Ⅰ型裂纹场建立了无需分区的统一控制方程并进行了浙近分析,利用“打靶法”得到位移场在物质描述与空间描述下的渐近阶次分别为3/4和1,Green应变、第二类P-K应力及Cauchy应力在物质描述与空间描述下的渐近阶次分别为-1/2和-2/3;对不同泊松比,裂尖有限变形线弹性场的位移均以U_Ⅱ或u_2为主导,裂纹张开角为π,现时构形中的大变形区为一垂直初始构形中裂纹表面的狭长带状区,应力则处于由σ_(22)主导的单向拉伸状态,角分布函数U_Ⅱ及σ_(22)(0)具有奇异性,但U_L/U_Ⅱ(0)及σ_(ij)(θ)/σ_(22)(0)均趋于有限值。
The unified asymptotic govering equations of the linear elastic crack fi elds of mode I with finite deformation were established without any demarcation schemes. By means of 'shooting method', the asymptotic orders of displacement were found to be 3/4 and 1 for Lagrangian and Eulerian descriptions re-specrtively. Those of Green strain, the second kind of P-K stress and Cauchy stress were found to be - 1/2 and - 2/3 under Lagrangian and Eulerian descriptions respectively. For different values of Pois-sion's ratio, the displacement is controlled by UII or u2 and the crack opening angle is n. The finite deformed linear elastic crack tip appears as a thin zone perpendicular to the initial undeformed crack surfaces and the stress is controlled by a22. The angular distribution functins UII (0) and 22(0) have singularity, but UL/UII(0) and ij 22(0) approach finite values.
出处
《力学季刊》
CSCD
北大核心
2001年第3期352-358,共7页
Chinese Quarterly of Mechanics
基金
河南省教育厅自然科学基础研究项目(98130001)
